Abstract
Let R be a commutative noetherian ring and a an ideal of R. The goal of this paper is to establish the local-global principle for the artinianness dimension r a ( M ) , where r a ( M ) is the smallest integer such that the local homology module of M is not artinian. For an artinian R-module M with the set Coass R H r a ( M ) a ( M ) finite, we show that r a ( M ) = inf { r a R p ( Hom R ( R p , M ) ) | p ∈ Spec R } . And the class of all modules N such that Coass R N is finite is studied.
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